The Origins of Infinitesimal Calculus

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Author: Margaret E. Baron

Publisher: Elsevier

ISBN: 1483280926

Category: Mathematics

Page: 312

View: 8264

The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.

The Historical Development of the Calculus

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Author: C.H.Jr. Edwards

Publisher: Springer Science & Business Media

ISBN: 1461262305

Category: Mathematics

Page: 368

View: 6529

The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.

A Treatise on Infinitesimal Calculus, Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics: Differential calculus. 1857.- v.2. Integral calculus, calculus of variations, and differential equations. 1865.- v.3. Statics and dynamics of material particles. 1856.- v.4. The dynamics of material systems. 1862

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Author: Bartholomew Price

Publisher: N.A

ISBN: N.A

Category: Calculus

Page: N.A

View: 9899

The Metaphysical Principles of the Infinitesimal Calculus

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Author: René Guénon

Publisher: Sophia Perennis

ISBN: 9780900588082

Category: Mathematics

Page: 132

View: 357

Gunon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet thread throughout his doctrinal studies. In this late text published just five years before his death, Gunon devotes an entire volume to questions regarding the nature of limits and the infinite with respect to the calculus both as a mathematical discipline and as symbolism for the initiatic path. This book therefore extends and complements the geometrical symbolism he employs in other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. According to Gunon, the concept 'infinite number' is a contradiction in terms. Infinity is a metaphysical concept at a higher level of reality than that of quantity, where all that can be expressed is the indefinite, not the infinite. But although quantity is the only level recognized by modern science, the numbers that express it also possess qualities, their quantitative aspect being merely their outer husk. Our reliance today on a mathematics of approximation and probability only further conceals the 'qualitative mathematics' of the ancient world, which comes to us most directly through the Pythagorean-Platonic tradition.

Sherlock Holmes in Babylon

And Other Tales of Mathematical History

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Author: Marlow Anderson,Victor Katz,Robin Wilson

Publisher: MAA

ISBN: 9780883855461

Category: Mathematics

Page: 387

View: 2472

Collection of essays on the history of mathematics by distinguished authorities.

The Origins of Cauchy's Rigorous Calculus

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Author: Judith V. Grabiner

Publisher: Courier Corporation

ISBN: 0486438155

Category: Mathematics

Page: 252

View: 8201

This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.

Infinitesimal Methods of Mathematical Analysis

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Author: J S Pinto

Publisher: Elsevier

ISBN: 0857099507

Category: Mathematics

Page: 270

View: 2753

This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro. Surveys modern reformulations of the infinitesimal concept with a comprehensive exposition of important and influential hyperreal numbers Includes material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis

The Calculus

A Genetic Approach

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Author: Otto Toeplitz

Publisher: University of Chicago Press

ISBN: 9780226806693

Category: Mathematics

Page: 201

View: 4868

When first published posthumously in 1963, this bookpresented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus. Reissued for the first time since 1981 and updated with a new foreword, this classic text in the field of mathematics is experiencing a resurgence of interest among students and educators of calculus today.

A treatise on infinitesimal calculus

containing differential and integral calculus, calculus of variations, applications to algebra and geometry, and analytical mechanics

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Author: Bartholomew Price

Publisher: N.A

ISBN: N.A

Category: Calculus of variations

Page: N.A

View: 3590

The Theory of Matrices

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Author: Cyrus Colton MacDuffee

Publisher: Courier Corporation

ISBN: 9780486495903

Category: Mathematics

Page: 110

View: 2112

This volume offers a concise overview of matrix algebra's many applications, discussing topics of extensive research and supplying proofs. Its contents include reviews of matrices, arrays, and determinants; the characteristic equation; associated integral matrices; equivalence, congruence, and similarity; composition of matrices; matric equations; functions of matrices; and matrices of infinite order. 1946 edition.

The Philosophy of Mathematics

Translated from Cours de Philosophie Positive by W. M. Gillespie

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Author: Auguste Comte

Publisher: Courier Corporation

ISBN: 0486155137

Category: Mathematics

Page: 272

View: 9479

Written by the nineteenth-century French philosophical founder of positivism, this comprehensive map of mathematical science assigns to each part of the complex whole its true position and value.

The General Theory of Dirichlet's Series

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Author: G. H. Hardy,Marcel Riesz

Publisher: Courier Corporation

ISBN: 048615517X

Category: Mathematics

Page: 96

View: 309

This classic work by two distinguished mathematicians explains theory and formulas behind Dirichlet's series and offers first systematic account of Riesz's theory of summation of series by typical means. 1915 edition.

Lectures on the Theory of Elliptic Functions

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Author: Harris Hancock

Publisher: Courier Corporation

ISBN: 9780486438252

Category: Mathematics

Page: 498

View: 5252

Prized for its extensive coverage of classical material, this text is also well regarded for its unusual fullness of treatment and its comprehensive discussion of both theory and applications. The author developes the theory of elliptic integrals, beginning with formulas establishing the existence, formation, and treatment of all three types, and concluding with the most general description of these integrals in terms of the Riemann surface. The theories of Legendre, Abel, Jacobi, and Weierstrass are developed individually and correlated with the universal laws of Riemann. The important contributory theorems of Hermite and Liouville are also fully developed. 1910 ed.

An Introduction to the Theory of Canonical Matrices

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Author: H. W. Turnbull,A. C. Aitken

Publisher: Courier Corporation

ISBN: 0486441687

Category: Mathematics

Page: 224

View: 9813

Elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. 1952 edition. 275 problems.